Diffusion coefficients in a lamellar lyotropic phase: evidence for defects connecting the surfactant structure

Unveiling the phase behavior of CiEj non-ionic surfactants in water through coarse-grained molecular dynamics simulations

Poly(oxyethylene) alkyl ethers, usually denoted by CiEj surfactants, exhibit a rich phase behavior in water, self-assembling to form a variety of 3-D structures with a controllable morphology that find multiple applications across different industrial segments. Hence, being able to describe and understand the effect of molecular structure on the phase behavior of these systems is highly relevant for the efficient design of new materials and their applications. Considering the promising results obtained over the last decade using the MARTINI model to describe ethylene-oxide containing compounds, an extensive assessment of the ability of such a model to describe the phase behavior of CiEj in water was carried out and results are presented here. Given the overall poor temperature transferability of the MARTINI model, mostly due to the lack of an accurate representation of hydrogen bonding, simulations were carried out at a single temperature of 333 K, where most phases are expected to occur according to experiments. Different chain lengths of both the hydrophobic and hydrophilic moieties, spanning a wide range of hydrophilic-lipophilic balance values, were investigated and the phase diagrams of various CiEj surfactants explored over a wide concentration range. The model was able to satisfactorily describe the effect of surfactant structure and concentration on mesophase formation. The stability and dimensions of the obtained phases, and the prediction of some unique features such as the characterization of a singular lamellar phase are presented. The results obtained in this work highlight both the predictive ability and the transferability of the MARTINI forcefield in the description of such systems. Moreover, the model was shown to provide adequate descriptions of the micellar phase in terms of micelle dimensions, critical micelle concentration, and average aggregation number.

Aqueous phase behavior of the PEO-containing non-ionic surfactant C12E6: A molecular dynamics simulation study

HYPOTHESIS

Non-ionic surfactants containing polyethylene oxide (PEO) chains are widely used in drug formulations, cosmetics, paints, textiles and detergents. High quality molecular dynamics models for PEO surfactants can give us detailed, atomic-scale information about the behavior of surfactant/water mixtures.

SIMULATIONS

We used two molecular dynamics force fields (FFs), 2016H66 and 53A6_DBW, to model the simple non-ionic PEO surfactant, hexaoxyethylene dodecyl ether (C₁₂E₆). We investigated surfactant/water mixtures that span the phase diagram of starting from randomly distributed arrangements. In some cases, we also started with prebuilt, approximate models. The simulations results were compared with the experimentally observed phase behavior.

FINDINGS

Overall, this study shows that the spontaneous self-assembly of PEO non-ionic surfactants into different colloidal structures can be accurately modeled with MD simulations using the 2016H66 FF although transitions to well-formed hexagonal phase are slow. Of the two FFs investigated, the 2016H66 FF better reproduces the experimental phase behavior across all regions of the C₁₂E_6/water phase diagram.

Dynamics of Dislocations in Smectic A Liquid Crystals Doped with Nanoparticles

Edge dislocations are linear defects that locally break the positional order of the layers in smectic A liquid crystals. As in usual solids, these defects play a central role for explaining the plastic properties of the smectic A phase. This work focuses on the dynamical properties of dislocations in bulk samples prepared between two glass plates and in free-standing films. The emphasis will be put on the measurement of the mobility of edge dislocations in liquid crystals either pure or doped with nanoparticles. The experimental results will be compared to the existing models.

Simulating Bilayers of Nonionic Surfactants with the GROMOS-Compatible 2016H66 Force Field

Polyoxyethylene glycol alkyl ether amphiphiles (C_iE_j) are important nonionic surfactants, often used for biophysical and membrane protein studies. In this work, we extensively test the GROMOS-compatible 2016H66 force field in molecular dynamics simulations involving the lamellar phase of a series of C_iE_j surfactants, namely C₁₂E₂, C₁₂E₃, C₁₂E₄, C₁₂E₅, and C₁₄E₄. The simulations reproduce qualitatively well the monitored structural properties and their experimental trends along the surfactant series, although some discrepancies remain, in particular in terms of the area per surfactant, the equilibrium phase of C₁₂E₅, and the order parameters of C₁₂E₃, C₁₂E₄, and C₁₂E₅. The polar head of the C_iE_j surfactants is highly hydrated, almost like a single polyethyleneoxide (PEO) molecule at full hydration, resulting in very compact conformations. Within the bilayer, all C_iE_j surfactants flip-flop spontaneously within tens of nanoseconds. Water-permeation is facilitated, and the bending rigidity is 4 to 5 times lower than that of typical phospholipid bilayers. In line with another recent theoretical study, the simulations show that the lamellar phase of C_iE_j contains large hydrophilic pores. These pores should be abundant in order to reproduce the comparatively low NMR order parameters. We show that their contour length is directly correlated to the order parameters, and we estimate that they should occupy approximately 7-10% of the total membrane area. Due to their highly dynamic nature (rapid flip-flops, high water permeability, observed pore formation), C_iE_j surfactant bilayers are found to represent surprisingly challenging systems in terms of modeling. Given this difficulty, the results presented here show that the 2016H66 parameters, optimized independently considering pure-liquid as well as polar and nonpolar solvation properties of small organic molecules, represent a good starting point for simulating these systems.

Solvent-free, molecular-level modeling of self-assembling amphiphiles in water

Aggregation mesophases of self-assembling amphiphiles in water are highly important in the context of biology (biomembranes), therapy (liposomes), industry (polymer surfactants), and condensed-matter physics (lyotropic liquid crystals). Besides helping to increase fundamental understanding of collective molecular behavior, simulations of these lyotropic phases are pivotal to technological and medical developments such as smart drug carriers for gene therapy. Implicit-solvent, coarse-grained, low resolution modeling with a simple pair potential is the key to realizing the larger length and time scales associated with such mesoscopic phenomena during a computer simulation. Modeling amphiphiles by directed, soft, ellipsoidal cores interacting via a computationally simple yet tunable anisotropic pair potential, we have come to such a single-site model amphiphile that can rapidly self-assemble to give diverse lyotropic phases (such as fluid bilayers, micelles, etc.) without requiring the explicit incorporation of solvent particles. The model directly represents a tunable packing parameter that manifests in the spontaneous curvature of the amphiphile aggregates. Besides the all-important hydrophobic interaction, the hydration force is also treated implicitly. Thanks to the efficient solvent-free molecular-level coarse graining, this model is suitable for generic mesoscale studies of phenomena such as self-assembly, amphiphile mixing, domain formation, fusion, elasticity, etc., in amphiphile aggregates.

Stability of C(12)E(j) Bilayers Probed with Adhesive Droplets

The stability of model surfactant bilayers from the poly(ethylene glycol) mono-n-dodecyl ether (C12Ej) family was probed. The surfactant bilayers were formed by the adhesion of emulsion droplets. We generated C12Ej bilayers by forming water-in-oil (w/o) emulsions with saline water droplets, covered by the surfactant, in a silicone and octane oil mixture. Using microfluidics, we studied the stability of those bilayers. C12E1 allowed only short-lived bilayers whereas C12E2 bilayers were stable over a wide range of oil mixtures. At high C12E2 concentration, a two-phase region was displayed in the phase diagram: bilayers formed by the adhesion of two water droplets and Janus-like particles consisting of adhering aqueous and amphiphilic droplets. C12E8 and C12E25 did not mediate bilayer formation and caused phase inversion leading to o/w emulsion. With intermediate C12E4 and C12E5 surfactants, both w/o and o/w emulsions were unstable. We provided the titration of the C12E2 bilayer with C12E4 and C12E5 to study and predict their stability behavior.

Molecular conformation and bilayer pores in a nonionic surfactant lamellar phase studied with 1H-13C solid-state NMR and molecular dynamics simulations

The structure of the lamellar phase of aqueous pentaethylene glycol mono-n-dodecyl ether (C12E5) surfactant at various temperatures and molar fractions is studied by using united atom molecular dynamics simulations and nuclear magnetic resonance measurements. Namely, the simulation model is used to interpret the magnitude and temperature dependence of experimental C-H order parameter profiles in terms of the molecular conformation and orientation. Our simulations suggest that the low order parameters that are generally measured in poly(ethylene oxide) surfactant bilayers are due to the presence of bilayer pores throughout the entire lamellar phase region.

Electric field alignment of a block copolymer nanopattern: direct observation of the microscopic mechanism

Using quasi-in-situ scanning force microscopy we study the details of nanopattern alignment in ABC terblock copolymer thin films in the presence of an in-plane electric field. Because of the surface interactions and electric field the lamellae are oriented both perpendicular to the plane of the film and parallel to the electric field. We identified two distinct defect types which govern the orientation mechanism. Ring-like (tori) and open-end defects dominate at the early stage of the orientation process, while mainly classic topological defects (disclinations and dislocations) are involved in long-range ordering at the late stages. Comparison of the time evolution of the defect density with the evolution of the orientational order parameter suggests that tori-defects are essential for the effective reorientation. Further, the quasi-in-situ SFM imaging allowed us to elucidate the influence of the electric field strength on the propagation velocity of the topological defects.

Kinetics of layer hopping in a diblock copolymer lamellar phase

In the ordered state, symmetric diblock copolymers self-assemble into an anisotropic lamellar morphology. The equilibrium thickness of the lamellae is the result of a delicate balance between enthalpic and entropic energies, which can be tuned by controlling the temperature. Here we devise a simple yet powerful method of detecting tiny changes in the lamellar thickness using optical microscopy. From such measurements we characterize the enthalpic interaction as well as the kinetics of molecules as they hop from one layer to the next in order to adjust the lamellar thickness in response to a temperature jump. The resolution of the measurements facilitate a direct comparison to predictions from self-consistent field theory.

Specific features of defect structure and dynamics in the cylinder phase of block copolymers

We present a systematic study of defects in thin films of cylinder-forming block copolymers upon long-term thermal or solvent annealing. In particular, we consider in detail the peculiarities of both classical and specific topological defects, and conclude that there is a strong "defect structure-chain mobility" relationship in block copolymers. In the systems studied, representative defect configurations provide connectivity of the minority phase in the form of dislocations with a closed cylinder end or classical disclinations with incorporated alternative, nonbulk structures with planar symmetry. In solvent-annealed films with enhanced chain mobility, the neck defects (bridges between parallel cylinders) were observed. This type of nonsingular defect has not been identified in block copolymer systems before. We argue that topological arguments and 2D defect representation, sufficient for lamellar systems, are not sufficient to determine the stability and mobility of defects in the cylindrical phase. In-situ scanning force microscopy measurements are compared with the simulations based on the dynamic self-consistent mean field theory. The close match between experimental measurements and simulation results suggests that the lateral defect motion is diffusion-driven. In addition, 3D simulations demonstrated that the bottom (wetting) layer is only weakly involved into the structure ordering at the free surface. Finally, the morphological evolution is considered with the focus on the motion and interaction of the representative defect configurations.

Broad-wavelength-range chemically tunable block-copolymer photonic gels

Responsive photonic crystals have been developed for chemical sensing using the variation of optical properties due to interaction with their environment. Photonic crystals with tunability in the visible or near-infrared region are of interest for controlling and processing light for active components of display, sensory or telecommunication devices. Here, we report a hydrophobic block-hydrophilic polyelectrolyte block polymer that forms a simple one-dimensional periodic lamellar structure. This results in a responsive photonic crystal that can be tuned via swelling of the hydrophilic layers by contact with a fluid reservoir. The glassy hydrophobic layer forces expansion of the hydrophilic layer along the layer normal, yielding extremely large optical tunability through changes in both layer thickness and index of refraction. Polyelectrolyte polymers are known to be highly responsive to a range of stimuli. We show very large reversible optical changes due to variation of the salt concentration of a water reservoir. These one-dimensional Bragg stacks reflect incident light from the ultraviolet-visible region to the near-infrared region (lambda(peak)=350-1,600 nm) with over a 575% change in the position of the stop band. Our work demonstrates the extremely high responsivity possible for polyelectrolyte-based photonic materials.

Effect of shear on an onion texture

Lamellar systems are self-assemblies of surfactant molecules forming planar bilayers separated by layers of solvent. At sufficiently high shear rates, they are known to form spherical objects often referred to as onions. In this paper, we are concerned with the effect of shear on those multi-lamellar vesicles. We measure solvent diffusion by nuclear magnetic resonance (NMR) using a method which is sensitive to the time dependence of mean-squared displacements. This method, combined with NMR velocimetry, allows us to infer onion structure as a function of shear rate, identifying different regimes in which local viscosity is related to the onion size. The role of slip is examined and the stress dependence of wall slip velocities is determined.

Evolution of a lamellar domain structure for an equilibrating lyotropic liquid crystal

Aerosol OT/water exhibits a lamellar phase over a wide range of concentrations. We show, by magnetic resonance (NMR) and scanning electron microscopy (SEM), that the morphology of the lamellar phase varies significantly across that range and that the rate of equilibration depends strongly on concentration (25, 33, and 50 wt %) with, paradoxically, the faster equilibration at higher surfactant concentrations. We find that the 25 wt % sample exhibits a defect-rich local structure, characteristic of a superposed L(3) character. Further into the lamellar region, at 33 wt %, this defect-rich structure persists heterogeneously, while, at 50 wt %, the lamellar phase domains are highly ordered. The NMR methods used here included (2)H spectroscopy and the two-dimensional NMR method, diffusion-diffusion exchange spectroscopy (DEXSY). The latter was used to obtain quantitative information on the domain sizes and defects within the polydomain lamellar mesophase. Comparison of the NMR with the SEM results suggests that, at 25 wt % AOT, bilayer defects play an important role in influencing the (2)H NMR and DEXSY NMR results.

Net charge and electrophoretic mobility of lysozyme charge ladders in solutions of nonionic surfactant

We report on the electrophoretic mobility and on the thermal diffusion of lysozyme proteins dissolved in aqueous solutions of a nonionic surfactant (C12E6) at a wide range of concentrations of the surfactant (0-20% by weight). We want to estimate the influence of a dense network of elongated micelles of C12E6 on the effective charge of the proteins as observed in the capillary electrophoresis experiments. The possible mechanism leading to the change in the effective charge of protein could involve the deformation of the cloud of counterions around the protein when it squeezes through the narrow (of the order of a protein diameter) aqueous channels formed in the solution of elongated micelles. The combination of independent measurements of the electrophoretic mobility of a family of modified proteins (lysozyme charge ladder [Colton et al. J. Am. Chem. Soc. 1997, 119, 12701]), of the microviscosity of the solutions of surfactant (obtained via fluorescence correlation spectroscopy), and of the hydrodynamic radius of the proteins (photon correlation spectroscopy) allow us to conclude that the effective charge of the proteins is not affected by the presence of surfactant, even at high concentrations.

Pores in bilayer membranes of amphiphilic molecules: coarse-grained molecular dynamics simulations compared with simple mesoscopic models

We investigate pores in fluid membranes by molecular dynamics simulations of an amphiphile-solvent mixture, using a molecular coarse-grained model. The amphiphilic membranes self-assemble into a lamellar stack of amphiphilic bilayers separated by solvent layers. We focus on the particular case of tensionless membranes, in which pores spontaneously appear because of thermal fluctuations. Their spatial distribution is similar to that of a random set of repulsive hard disks. The size and shape distribution of individual pores can be described satisfactorily by a simple mesoscopic model, which accounts only for a pore independent core energy and a line tension penalty at the pore edges. In particular, the pores are not circular: their shapes are fractal and have the same characteristics as those of two-dimensional ring polymers. Finally, we study the size-fluctuation dynamics of the pores, and compare the time evolution of their contour length to a random walk in a linear potential.

Movement of Proteins in an Environment Crowded by Surfactant Micelles: Anomalous versus Normal Diffusion

Small proteins move in crowded cell compartments by anomalous diffusion. In many of them, e.g., the endoplasmic reticulum, the proteins move between lipid membranes in the aqueous lumen. Molecular crowding in vitro offers a systematic way to study anomalous and normal diffusion in a well controlled environment not accessible in vivo. We prepared a crowded environment in vitro consisting of hexaethylene glycol monododecyl ether (C(12)E(6)) nonionic surfactant and water and observed lysozyme diffusion between elongated micelles. We have fitted the data obtained in fluorescence correlation spectroscopy using an anomalous diffusion model and a two-component normal diffusion model. For a small concentration of surfactant (below 4 wt %) the data can be fitted by single-component normal diffusion. For larger concentrations the normal diffusion fit gave two components: one very slow and one fast. The amplitude of the slow component grows with C(12)E(6) concentration. The ratio of diffusion coefficients (slow to fast) is on the order of 0.1 for all concentrations of surfactant in the solution. The fast diffusion is due to free proteins while the slow one is due to the protein-micelle complexes. The protein-micelle interaction is weak since even in a highly concentrated solution (35% of C(12)E(6)) the amplitude of the slow mode is only 10%, despite the fact that the average distance between the micelles is the same as the size of the protein. The anomalous diffusion model gave the anomaly index (r(2)(t) approximately t(alpha)), alpha monotonically decreasing from alpha = 1 (at 4% surfactant) to alpha = 0.88 (at 37% surfactant). The fits for two-component normal diffusion and anomalous diffusion were of equally good quality, but the physical interpretation was only straightforward for the former.

Undulations and fluctuations in a lamellar phase lyotropic liquid crystal and their suppression by weak shear flow

Using multi-echo pulsed gradient nuclear magnetic resonance (NMR) we measure the anisotropic diffusion of water molecules in the lamellar phase of lyotropic system composed of cetylpyridinium chloride/hexanol diluted in brine. The technique reveals the Fourier spectrum of the molecular velocity autocorrelation function, and its repetitive compensating nature permits effective measurement in the presence of shear flow. We show that under zero shear the phase is highly oriented and that both the amplitude and fluctuation correlation time of lamellar undulations can be measured. The suppression of undulations by weak shear is apparent. We further measure transverse lamellae permeability arising from defects.

Role of dislocation loops on the elastic constants of lyotropic lamellar phases

We study the role of dislocation loops defects on the elasticity of lamellar phases by investigating the variation of the lamellar elastic constants, B and K, induced by the proliferation of these defects. We focus our interest on one particular lamellar phase made up of a mixture of C(12)E(5) and DMPC in water, which is already well-characterised. This lamellar phase undergoes a second-order (or weakly first-order) lamellar-to-nematic phase transition at about 19 degrees C and dislocation loops are seen to proliferate within the lamellar structure when temperature is decreased below 30 degrees C. The values of both elastic constants of this given lamellar phase are measured as a function of temperature, approaching the lamellar-to-nematic transition, with the help of Quasi-Elastic Light Scattering (QELS) on oriented lamellar phases. Very surprisingly we observe a strong and rapid increase in both Band K as the lamellar-to-nematic transition temperature is approached. These increases are seen to start as soon as dislocation loops can be observed in the lamellar phase. We interpret our results as being the consequence of the appearance and proliferation of dislocation loops within the lamellar structure. According to a simple model we developed we show that B and K are proportional to the density of dislocation loops in the lamellar phase.

A study of anisotropic water self-diffusion and defects in the lamellar mesophase

The correlation of molecular diffusion coefficients obtained via a novel two-dimensional pulsed gradient spin-echo (PGSE) NMR method has been shown to reveal detailed structural information on the mesophases of lyotropic liquid crystals. A four-component system containing both nonionic (pentaethylene glycol monododecyl ether) and ionic (sodium dodecyl sulfate) surfactants, water, and decane was prepared and left to equilibrate. In the temperature region around 309 K, a lamellar mesophase forms. A two-dimensional Laplace inverse transformation was performed on the (gammadeltag)2(delta - delta/3) domain data to separate any multiexponential behavior that resulted from local anisotropy. The results of the double PGSE experiment with contiguous gradient pulse pairs, applied both collinearly and orthogonally, clearly show the presence of local anisotropic self-diffusion of the water molecules and suggest a preferred orientation of the lamellae. Information about defects/domain size was obtained by the insertion of a mixing time (t(m)') between the successive gradient pulse pairs. This work highlights the value of this new NMR correlation method in the study of surfactant systems.

An NMR study of translational diffusion and structural anisotropy in magnetically alignable nonionic surfactant mesophases

The diffusion of both water and surfactant components in aqueous solutions of the nonionic surfactant "C12E6"--which includes hexagonal, cubic, lamellar, and micellar mesophases--has been studied by pulsed-field-gradient NMR. Diffusion coefficients were measured in unaligned samples in all of these phases. They were also obtained in the hexagonal and lamellar phases in oriented monodomain samples that were aligned by slow cooling from the micellar phase in an 11.7 T magnet. Measured water and soap diffusion coefficients in the NMR-isotropic cubic and (high-water-content) micellar phases as well as diffusion anisotropy measurements in the magnetically aligned hexagonal phase were quantitatively consistent with the constituent structures of these phases being identical surfactant cylinders, with only the fraction of surface-associated water varying with the water-soap molar ratio. The values of the water and soap diffusion coefficients in the oriented lamellar phase suggest an increase in defects and obstructions to soap diffusion as a function of increasing water content, while those in the low-water-content micellar phase rule out the presence of inverse micelles.

Bounded step superdiffusion in an oriented hexagonal phase

Fluorescence recovery after pattern photobleaching is used to measure the self-diffusion of surfactant molecules, along cylinders and perpendicular to their main axis in an oriented hexagonal lyotropic phase. Unexpectedly, while the motion along cylinders is diffusive, a superdiffusive behavior is observed in the direction perpendicular to the cylinder axis. Moreover, varying the lattice parameter, we found that the perpendicular diffusion time is governed only by the number of cylinders to cross, providing experimental evidence for superdiffusion with a bounded step length.

Morphological changes during the order-disorder transition in the two- and three-dimensional systems of scalar nonconserved order parameters

The order-disorder transition is studied in a system of a scalar nonconserved order parameter. We use this well studied system to show that the application of the methods of topology and geometry reveals that our knowledge of the kinetic pathways by which the order-disorder transition proceeds is far from being complete. We show that in two-dimensional (2D) and 3D systems there are three dynamical regimes in the evolution of the system: early, intermediate, and late. In the intermediate regime two length scales govern the behavior of the system, whereas in the early and intermediate regime there is only one length scale. The size distribution of the domain area indicates the pathway by which the domains change their size. There are only two types of domains in a 2D system: circular and elongated with well defined characteristics (scaling of the area with the contour length) which in the late regime do not depend on time after rescaling by the average area and contour in the system. The elongated domains continuously change into circular domains reducing in this way the overall dissipation in the system. In order to reach a Lifshitz-Cahn-Allen (LCA) late stage regime the number of elongated domains must be strongly reduced. In the intermediate regime the number of elongated domains is large and simple LCA scaling does not hold. In a 3D symmetric system we always have a bicontinuous structure that evolves by cutting small connections. The late stage regime seems to be associated with the appearance of the preferred nonzero mean curvature. The early-intermediate regime crossover is associated with the saturation of the order parameter inside the domains, while the intermediate-late stage regime crossover is related to the global breaking of the +/- order parameter symmetry (marked by the appearance of the nonzero mean curvature but still zero average magnetization). The times for the occurrence of these crossovers do not depend on the size of the system.

Tracer diffusion in a dislocated lamellar system

Many lamellar systems exhibit strongly anisotropic diffusion. When the diffusion across the lamellae is slow, an alternative mechanism for transverse transport becomes important. A tracer particle can propagate across the lamellae by encircling a screw dislocation. We calculate the statistical properties of this mode of transverse transport. When either positive or negative dislocations are in excess, transport across the lamellae is ballistic. When the average dislocation charge is zero, the mean square of the normal displacement grows like TlogT for large times. To obtain this result, the trajectory of the tracer must be smoothed over distances of order of the dislocation core size.